On the basis of the recommendations of the ESD Computer Security Technology Panel techniques were developed for the design, implementation, and formal mathematical verification of a security kernel: a hardware and software mechanism to control access to information within a computer system. This three- volume report describes the design of a security kernel for the Honeywell Information Systems Multics computer system. This first volume gives a methodology and design overview. The primary subsystems are defined, and the reasoning behind the design decisions is given. The correspondence of the design to a mathematical model is discussed, giving a preview to the formal verification. The second volume gives a formal top-level specification of the primary subsystems. The third volume deals with the secondary subsystems, including the issues of initialization and reconfiguration.